The Spectra of Volume and Determinant Densities of Links

2015/07/07 by Burton, Stephan D.
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1507.01954

Abstract

The volume density of a hyperbolic link K is defined to be the ratio of the hyperbolic volume of K to the crossing number of K. We show that there are sequences of non-alternating links with volume density approaching v₈, where v₈ is the volume of the ideal hyperbolic octahedron. We show that the set of volume densities is dense in [0,v₈]. The determinant density of a link K is [2 πlog det(K)]/c(K). We prove that the closure of the set of determinant densities contains the set [0, v₈].

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